XXXVII. and XXXVIII., which contain some statistics for Batavia due to van Bemmelen, and some for Greenwich derived from the data in Maunders. papers referred to above. Table XXXVII. gives the relative frequency of occurrence for two hour intervals, starting with midnight, treating separately the storms of gradual (g) and sudden (s) commencement. In Table XXXVIII. the day is subdivided into three equal parts. Batavia and Greenwich agree in showing maximum frequency of beginnings about the time of minimum frequency of endings and conversely; but the hours at which the respective maxima and minima occur at the two places differ rather notably.
§ 36. There are peculiarities in the sudden movements ushering in magnetic storms which deserve fuller mention. According to van Bemmelen the impulse consists usually at some stations of a sudden slight jerk of the magnet in one direction, followed by a larger decided movement in the opposite direction, the former being often indistinctly shown. Often we have at the very commencement but a faint outline, and thereafter a continuous movement which is only sometimes distinctly indicated, resulting after some minutes in the displacement of the trace by a finite amount from the position it occupied on the paper before the disturbance began.
Total Percentages. {
Number. Winter. Equinox. Summer.
Greenwich disturbed days,
all, 1848—1902 4,214 33'9 39'2 26.9
Greenwich disturbed days,
range To' to 3o', 1848
1902 . . . 3,830 33'9 39.0 27.1
Greenwich disturbed days,
range 30' to 6o', 1848
1902 • . . 307 34'5 41.0 24.4
Greenwich disturbed days,
range over 6o', 1848
1902 . . . 77 29'9 41.6 28.6
Kew highly disturbed days,
1 890—1900 . . . 209 38.3 41.6 20.1
Greenwich magnetic
storms, all, 1848—1903 . 726 32.1 42'3 25.6
Greenwich magnetic
storms, range 20' to 30',
1848—1903 . . . . 392 30.1 43.6 26.3
Greenwich magnetic
storms, range over 30',
1848—1903 . . . . 334 34'4 40'7 24.9
Greenwich m a g net i c
storms, all, 14 years of
S. max 258 35.3 38.0 26.7
Greenwich magnetic
storms, all, 15 years of
S. min 127 28.4 48'0 23.6
Batavia magnetic storms,
all, 1883—1899 . 1,008 32'9 34'9 32'2
Batavia magnetic storms
of gradual commence-
ment . . . . 679 32'4 34.8 32'8
Batavia magnetic storms
of sudden commence-
ment 329 33'7 35'3 31'0
This may mean, as van Bemmelen supposes, a small preliminary movement in the opposite direction to the clearly shown displacement; but it may only mean that the magnet is initially set in vibration, swinging on both sides of the position of equilibrium, the real displacement of the equilibrium position being all the time in the direction of the displacement apparent after a few minutes. To prevent misconception, the direction of the displacement apparent after a few minutes has been termed the direc-
Hour. o 2 4 6 8 10 12 14 16 18 20 22
Beginning g 5 5 5 6 zo 16 7 5 6 9 8 8
S 7 5 7 IO IO II IO 8 8 9 8 7
Maximum ( g 12 10 6 5 4 9 9 6 6 6 12 15
S 14 7 5 2 2 9 9 5 8 10 13 16
End all 15 16 , 19 13 5 3 6 5 4 5 4 5
tion of the first decided movement in Table XXXIX., which contains some data as to the direction given by Ellis 41 and van Bemmelen." The + sign means an increase, the — sign a decrease of the element. The sign is not invariably the same, it will be understood, but there are in all cases a marked preponderance of changes in the direction shown in the table. The fact that all the stations indicated an increase in horizontal force is of special significance.
Epoch. Class. Total Percentages.
Number.
1—8 p.m. 9 4 a.m. noon.
Begin- ` 1848—1903 all 721 60•, 21 9 I8 o
1882 -1903 276 580 188 23.2
mng lj sudden 77 45'4 27'3 27'3
,,
1 848—19o3 all 720 9'4 44'6 46.0
End 1882—1903 7 z 41 7 51.1
sudden 276
77
11'7 35.1 53.2
§ 37. That large magnetic disturbances occur simultaneously over large areas was known in the time of Gauss, on whose initiative observations were taken at 5-minute intervals at a number of stations
on prearranged term days. During March 1879 and August 1880 some large magnetic storms occurred, and the magnetic curves showing these at a number of stations fitted with Kew pattern magnetographs were compared by W. G. Adams.42 He found the more characteristic movements to be, so far as could be judged, simultaneous at all the stations. At comparatively near stations
Place. Declination. Horizontal Force. Vertical Force.
Pavlovsk West + +
Potsdam West + —
Greenwich West + +
Zi-ka-wei East + -
Kolaba East + -
Batavia West + -
Mauritius East + +
Cape Horn West + —
such as Stonyhurst and Kew, or Coimbra and Lisbon, the curves were in general almost duplicates., At Kew and St Petersburg there were usually considerable differences in detail, and the movements were occasionally in opposite directions. The differences between Toronto, Melbourne or Zi-ka-wei and the European stations were still more pronounced. In 1896, on the initiative of M. Eschenhagen,43 eye observations of declination and horizontal force were taken at 5-second intervals during prearranged hours at Batavia, Manila, Melbourne and nine European stations. The data from one of these occasions when appreciable disturbance prevailed were published by Eschenhagen, and were subsequently analysed by Ad. Schmidt.44 Taking the stations in western Europe, Schmidt drew several series of lines, each series representing the disturbing forces at one instant of time as deduced from the departure of the elements at the several stations from their undisturbed value. The lines answering to any one instant had a general sameness of direction with more or less divergence or convergence, but their general trend varied in a way which suggested to Schmidt the passage of a species of vortex with large but finite velocity.
The conclusion that magnetic disturbances tend to follow one another at nearly equal intervals of time has been reached by several independent observers. J. A. Broun45 pronounced for a period of about 26 days, and expressed a belief that a certain zone, or zones, of the sun's surface might exert a prepotent influence on the earth's magnetism during several solar rotations. Very similar views were advanced in 1904 by E. W. Maunder,39 who was wholly unaware of Broun's work. Maunder concluded that the period was 27.28 days, coinciding with the sun's rotation period relative to an observer on the earth. Taking magnetic storms at Greenwich from 1882 to 1903, he found the interval between the commencement of successive storms to approach closely to the above period in a considerably larger number of instances than one would have expected from mere chance. He found several successions of three or four storms, and in one instance of as many as six storms, showing his interval. In a later paper Maunder reached similar results for magnetic storms at Greenwich from 1848 to 1881. Somewhat earlier than Maunder, Arthur Harvey46 deduced a period of 27.246 days from a consideration of magnetic disturbances at Toronto. A. Schuster,47 examining Maunder's data mathematically, concluded that they afforded rather strong evidence of a period of about i (27.28) or 13.6 days. Maunder regarded his results as demonstrating that magnetic disturbances originate in the sun. He regarded the solar action as arising from active areas of limited extent on the sun's surface, and as propagated along narrow, well defined streams. The active areas he believed to be also the seats of the formation of sun-spots, but believed that their activity might precede and outlive the visible existence of the sun-spot.
Maunder did not discuss the physical nature of the phenomenon, but his views are at least analogous to those propounded somewhat earlier by Svante Arrhenius,48 who suggested that small negatively charged particles are driven from the sun by the repulsion of light and reach the earth's atmosphere, setting up electrical currents, manifest in aurora and magnetic disturbances. Arrhenius's calculations, for the size of particle which he regarded as most probable, make the time of transmission to the earth slightly under two days. Amongst other theories which ascribe magnetic storms to direct solar action may be mentioned that of Kr. Birkeland,49 who believes the vehicle to be cathode rays. Ch. Nordmann60 similarly has suggested Rontgen rays. Supposing the sun the ultimate source, it would be easier to discriminate between the theories if the exact time of the originating occurrence could be fixed. For instance, a disturbance that is propagated with the velocity of light may be due to Rontgen rays, but not to Arrhenius's particles. In support of his theory, Nordmann mentions several cases when conspicuous visual phenomena on the sun have synchronized with magnetic movements on the earth—the best known instance being the apparent coincidence in time of a magnetic disturbance at Kew on the 1st of September 1859 with a remarkable solar outburst seen by R. C. Carrington. Presumably any electrical phenomenon on the sun will set up waves in the aether, so transmission of electricand magnetic disturbances from the sun to the earth with the velocity .of light is a certainty rather than a, hypothesis; but it by no means follows that the energy thus transmitted can give rise to sensible magnetic disturbances. Also, when considering Nordmann's coincidences, it must be remembered that magnetic movements are so numerous that it would be singular if no apparent coincidences had been noticed. Another consideration is that the movements shown by ordinary magnetographs are seldom very rapid. During some. storms, especially those accompanied by unusually bright and rapidly varying auroral displays, large to and fro movements follow one another in close succession, the changes being sometimes too quick to be registered distinctly on the photographic paper. This, however, is exceptional, even in polar regions where disturbances are largest and most numerous. As a rule, even when the change in the direction of movement in the declination needle seems quite sudden, the movement in one direction usually lasts for several minutes, often for 1o, 15 or 30 minutes. Thus the cause to which magnetic disturbances are due seems in many cases to be persistent in one direction for a considerable time.
§ 38. Attempts have been made to discriminate between the theories as to magnetic storms by a critical examination of the phenomena. A general connexion between sun-spot frequency and the amplitude of magnetic movements, regular and irregular, is generally admitted. If it is a case of cause and effect, and the interval between the solar and terrestrial phenomena does not exceed a few hours, then there should be a sensible connexion between corresponding daily values of the sun-spot frequency and the magnetic range. Even if only some sun-spots are effective, we should expect when we select from a series of years two groups of days, the one containing the days of most sun-spots, the other the days of least, that a prominent difference will exist between the mean values of the absolute daily magnetic ranges for the two groups. Conversely, if we take out the days of small and the days of large magnetic range, or the days that are conspicuously quiet and those that are highly disturbed, we should expect a prominent difference between the corresponding mean sun-spot areas. An application of this principle was made by Chree43 to the five quiet days a month selected by the astronomer royal between 1890 and 1900. These days are very quiet relative to the average day and possess a much smaller absolute range. One would thus have expected on Birkeland's or Nordmann's theory the mean sun-spot frequency derived from Wolfer's provisional values for these days to be much below his mean value, 41.22, for the eleven years. It proved, however, to be 41.28. This practical identity was as visible in 1892 to 1895, the years of sun-spot maximum, as it was in the years of sun-spot minimum. Use was next made of the Greenwich projected sun-spot areas, which are the result of exact measurement. The days of each month were divided into three groups, the first and third—each normally of ten days—containing respectively the days of largest and the days of least sun-spot area. The mean sun-spot area from group 1 was on the average about five times that for group 3. It was then investigated how the astronomer royal's quiet days from 1890 to 1900, and how the most disturbed days of the period selected from the Kew24 magnetic records, distributed themselves among the three groups of days. Nineteen months were excluded, as containing more than ten days with no sun-spots. The remaining 113 months contained 565 quiet and 191 highly disturbed days, whose distribution was as follows:
Group 1. Group 2. Group 3.
Quiet days 179 195 191
Disturbed days 68 65 58
The group of days of largest sun-spot area thus contained slightly under their share of quiet days and slightly over their share of disturbed days. The differences, however, are not large, and in three years, viz. 1895, 1897 and 1899, the largest number of disturbed days actually occurred in group 3, while in 1895, 1896 and 1899 there were fewer quiet days in group 3 than in group 1. Taking the same distribution of days, the mean value of the absolute daily range of declination at Kew was calculated for the group 1 and the group 3 days of each month. The mean range from the group I days was the larger in 57% of the individual months as against 43 % in which it was the smaller. When the days of each month were divided into groups according to the absolute declination range at Kew, the mean sun-spot area for the group i days (those of largest range) exceeded that for the group 3 days (those of least range) in 55% of the individual months, as against 45% of cases in which it was the smaller.
Taking next the five days of largest and the five days of least range in each month, sun-spot areas were got out not merely for these days themselves, but also for the next subsequent day and the four immediately preceding days in each case. On Arrhenius's theory we should expect the magnetic range to vary with the sun-spot area, not on the actual day but two days previously. The following figures give the percentage excess or deficiency of the mean sun-spot area for the respective groups of days, relative to the average value for the whole epoch dealt with. n denotes the day to which the magnetic range belongs, n+1 the day after, n—i the day before, and
so on. Results are given for 1894 and 1895, the years which were on the whole the most favourable and the least favourable for Arrhenius's hypothesis, as well as for the whole eleven years.
Day. n-4 n-3 n-2 n-I n n+I
Five days of l 1894 +12 + 9 +11 +12 +11 +6
Five -16 -17 -15 -12 -II -10
95
largest range II yrs. + 9 + 8 + 8 + 7 + 5 +0.5
J(
Five days of 1894 -I5j -17 -19 -2I -2I -19
least range II yrs. x-14 - 4 - 7' - 7 - 7 - 4
Taking the II-year-means we have the sun-spot area practically normal on the day subsequent to the representative day of large magnetic range, but sensibly above its mean on that day and still more so on the four previous days. This suggests an emission from the sun taking a highly variable time to travel to the earth. The 11-year mean data for the five days of least range seem at first sight to point to the same conclusion, but the fact that the deficiency in sun-spot area is practically as prominent on the day after the representative day of small magnetic range as on that day itself, or the previous days, shows that the phenomenon is probably a secondary one. On the whole, taking into account the extraordinary differences between the results from individual years, we seem unable to come to any very positive conclusion, except that in the present state of our knowledge little if any clue is afforded by the extent of the sun's spotted area on any particular day as to the magnetic conditions on the earth on that or any individual subsequent day. Possibly some more definite information might be extracted by considering the extent of spotted area on different zones of the sun. On theories such as those of Arrhenius or Maunder, effective bombardment of the earth would be more or less confined to spotted areas in the zones nearest the centre of the visible hemisphere, whilst all spots on this hemisphere contribute to the total spotted area. Still the projected area of a spot rapidly diminishes as it approaches the edge of the visible hemisphere, i.e. as it recedes from the most effective position, so that the method employed above gives a preponderating weight to the central zones. One rather noteworthy feature in Table XL. is the tendency to a sequence in the figures in any one row. This seems to be due, at least in large part, to the fact that days of large and days of small sun-spot area tend to occur in groups. The same is true to a certain extent of days of large and days of small magnetic range, but it is unusual for the range to be much above the average for more than 3 or 4 successive days.
§ 39. The records from ordinary magnetographs, even when run at the usual rate and with normal sensitiveness, not infrequently show Pulsations. a repetition of regular or nearly regular small rhythmic
movements, lasting sometimes for hours. The amplitude and period on different occasions both vary widely. Periods of 2 to 4 minutes are the most common. W. van Bemmelen” has made a minute examination of these movements from several years' traces at Batavia, comparing the results with corresponding
statistics sent him from Zi-ka-wei and Kew. Table XLI. shows the diurnal variation in the frequency of occurrence of these small movements—called pulsations by van Bemmelen—at these three stations. The Batavia results are from the years 1885 and 1892 to 1898. Of the two sets of data for Zi-kawei (i) answers to the years 1897, 1898 and 1900, as given by van Bemmelen, while (ii) answers to the period 1900-1905, as given in the Zi-ka-wei Bulletin for 1905. The Kew data are for 1897. The results are expressed as percentages of the total for the 24 hours. There is a remarkable contrast between Batavia and Zi-ka-wei on the one hand and Kew on the other, pulsations being much more numerous by night than by day at the two former stations, whereas at Kew the exact reverse holds. Van Bemmelen decided that almost all the occasions of pulsation at Zi-ka-wei were also occasions of pulsations at Batavia. The hours of commencement at the two places usually differed a little, occasionally by as much as 20 minutes; but this he ascribed to the fact that the earliest oscillations were too small at one or other of the stations to be visible on the trace. Remarkable coincidence between pulsations at Potsdam and in the north of Norway has been noted by Kr. Birkeland.49
With magnetographs of greater sensitiveness and more open time scales, waves of shorter period be-come visible. In 1882 F. Kohlrausch" detected waves with a period of about 12 seconds. Eschenhagen" observed a great variety of short period waves, 30 seconds being amongst the most common. Some of the records he obtained suggest the superposition of regular sine waves of different periods. Employing a very sensitive galvanometer torecord changes of magnetic induction through a coil traversed by the earth's lines of force, H. Ebert" has observed vibrations whose periods are but a small fraction of a second. 'Frye observations of Kohlrausch and Eschenhagen preceded the recent great development of applications of electrical power, while longer period waves are shown in the Kew curves of 5o years ago, so that the existence of natural waves with periods of from a few seconds up to several minutes can hardly be doubted. Whether the much shorter period waves of Ebert are also natural is more open to doubt, as it is becoming exceedingly difficult in civilized countries to escape artificial disturbances.
Hours. 0-3. 3-6. 6-9. 9-Noon. I Noon-3. 3-6. 6-9. ,9-I2.
Batavia 28 9 2 6 8 6 13 28
Zi-ka-wei(i) 33 5 2 7 4 4 10 35
„ (ii) 23 6 8 II 7 5 14 26
Kew . 4 8 19 14 22 18 tii 4
§ 40. The fact that the moon exerts a small but sensible effect on the earth's magnetism seems to have been first discovered in 1841 by C. Kreil. Subsequently Sabine" investigated the nature of the lunar diurnal variation in declination Lunar at Kew, Toronto, Pekin, St Helena, Cape of Good Hope Influence. and Hobart. The data in Table XLII. are mostly due to Sabine. They represent the mean lunar diurnal inequality in declination for the whole year. The unit employed is o'•ooi, and as in our previous tables + denotes movement to the west. By " mean departure " is meant the arithmetic mean of the 24 hourly departures from the mean value for the lunar day; the range is the difference between the algebraically greatest and least of the hourly values. Not infrequently the mean departure gives the better idea of the importance of an inequality, especially when as in the present case two maxima and minima occur in the day. This double daily period is unusually prominent in the case of the lunar diurnal inequality, and is seen in the other elements as well as in the declination.
Lunar action has been specially studied in connexion with observations from India and Java. Broun55 at Trivandrum and C. Chambers 57 at Kolaba investigated lunar action from a variety of aspects. At Batavia van der Stole" and more recently S. Figee 59 have carried out investigations involving an enormous amount of computation. Table XLIII. gives a summary of Figee's results for the mean lunar diurnal inequality at Batavia, for the two half-yearly periods April to September (Winter or W.), and October to March (S.). The + sign denotes movement to the west in the case of declination, but numerical increase in the case of the other elements. In the case of H and T (total force) the results for the two seasons present comparatively small differences, but in the case of D, I and V the amplitude and phase both differ widely. Consequently a mean lunar diurnal variation derived from all the months of the year gives at Batavia, and presumably at other
Lunar Kew. Toronto. Batavia. St Helena. Cape. Hobart.
Hour. 1858-1862. 1843-1848. 1883-1899. 1843-1847. 1842-1846. 1841-1848.
o +103 +315 -70 - 43 -148 - 98
+ 160 +275 -63 - 5 -107 -138
2 +140 +158 -39 + 37 - 35 -142
3 + 33 + 2 - 8 + 70 + 43 -107
4 + lo -153 +38 + 85 +108 - 45
5 - 67 -265 +63 + 77 +140 + 27
6 -150 -302 +87 + 48 +132 + 88
7 -188 -255 +77 + 5 + 82 +122
8 -16o -137 +40 - 43 + 5 + 120
9 - 78 + 7 - 4 - 82 - 78 + 82
10 + 2 +178 -45 -102 -143 + 17
II + 92 +288 -8o - 98 -177 - 57
12 +160 +323 - 87 - 73 -165 -120
13 +188 +272 -68 - 32 -112 -152
14 +158 +148 -43 + 13 - 30 -147
15 + 90 - 17 - 8 + 52 + 58 -105
16 + to -18o +30 + 73 +132 - 35
17 - 85 -297 +62 + 73 +172 + 45
18 -142 -337 +72 + 52 +168 +112
19 -163 -290 +68 + 17 +122 +152
20 -147 -170 +52 - 25 + 45 +152
21 -123 - 7 + 8 - 58 - 40 +113
22 - 40 +155 -28 - 73 -112 + 47
23 + 27 +265 - 56 - 68 -153 - 30
Mean De- 105 200 50 54 104 93
parture
Range . 376 66o 174 187 349 304
Declination Inclination,S. H. V. T.
(unit o'•ooI). (unit o'•ooI). (unit 0.017). (unit 0.017). (unit 0.017).
Lunar W S. W. S. W. S. W. S. W. S.
Hour.
o +30 -170 — I +25 -15 — 56 — 9 + 4 — 17 -47
1 +21 -147 -23 +49 -40 — 87 -54 +20 61 -67
,-
2 + 5 — 83 -49 +69 -25 -107 -82 +37 - 62 -76
3 — 5 — 12 -51 +47 -21 — 76 -83 +24 — 59 -55
4 + I + 76 -37 +43 -13 — 59 -58 +18 — 39 -38
5 — 8 +134 -23 +12 +10 — 9 -27 +11 — 4 — 3
6 — 7 +181 — 2 -21 +21 + 43 + 9 — 6 + 23 +35
7 -10 +164 +30 -12 +23 + 45 +55 + 8 + 47 +43
8 — 7 + 86 +36 -21 +38 + 52 +71 — I + 68 +45
9 — 8 o +28 -23 +46 + 30 +64 -16 + 71 +19
10 — 5 — 85 +34 -20 +13 + 13 +54 -21 + 38 + 1
11 -15 -144 +27 —II —I2 — 6 +31 -19 + 5 -15
12 — 9 -164 +19 — 5 -47 -23 0 -19 -41 -29
13 +I -136 -3 +17 -59 -46 -36 -2 -69 -41
14 — 7 — 79 -13 +27 -66 — 44 -55 +14 — 84 -32
15 — 8 — 8 -32 +25 -53 — 37 -74 +14 — 82 -26
16 -12 + 72 -37 +25 -34 — 17 -70 +26 — 64 — 2
17 -13 +137 -33 + 4 — I + z8 -47 +21 — 24 +35
18 -2I +165 — 2 -10 +20 + 47 + 8 +12 + 21 +47
19 -12 +147 +21 -42 +44 + 81 +53 -14 + 64 +64
20 +10 + 95 +21 -62 +75 +107 +71 -28 +100 +80
21 +13 + 4 +26 -70 +65 + 98 +72 -44 + 92 +65
22 +25 — 82 +35 -41 +35 + 35 +68 -38 + 64 +12
23 +36 -147 +34 — 4 — 7 — 14 +44 -13 + 15 -19
Mean De- 12 150 26 29 33 48 50 18 51 37
parture
Range 57 351 87 139 141 214 155 81 184 156
tropical stations, an inadequate idea of the importance of the lunar influence. In January Figee finds for the range of the lunar diurnal inequality o.62 in D, 3.I7 in H and 3.5y in V, whereas the corresponding ranges in June are only 0'•13, I•Iy and 2.27 respectively. The difference between summer and winter is essentially due to solar action, thus the lunar influence on terrestrial magnetism is clearly a somewhat complex phenomepon. From a study of Trivandrum data, Broun concluded that the action of the moon is largely dependent on the solar hour at the time, being on the average about twice as great for a day hour as for a night hour. Figee s investigations at Batavia point to a similar conclusion. Following a method suggested by Van der Stok, Figee arrives at a numerical estimate of the " lunar activity " for each hour of the solar day, expressed in terms of that at noon taken as loo. In summer, for instance, in the case of D he finds the " activity " varying from 114 at to a.m. to only 8 at 9 p.m.; the corresponding extremes in the case of H are 139 at to a.m. and 54 at 6 a.m.
The question whether lunar influence increases with sun-spot frequency is obviously of considerable theoretical interest. Balfour Stewart in the 9th edition of this encyclopaedia gave some data indicating an appreciably enhanced lunar influence at Trivandrum during years of sun-spot maximum, but he hesitated to accept the result as finally proved. Figee recently investigated this point at Batavia, but with inconclusive results. Attempts have also been made to ascertain how lunar influence depends on the moon's declination and phase, and on her distance from the earth. The difficulty in these investigations is that we are dealing with a small effect, and a very long series of data would be required satisfactorily to eliminate other periodic influences. .
§ 41. From an analysis of seventeen years data at St Petersburg and Pavlovsk, Leyst60 concluded that all the principal planets
Planetary
sensibly influence the earth's magnetism. According to influence. his figures, all the planets except Mercury—whose in-
fluence he found opposite to that of the others—when nearest the earth tended to deflect the declination magnet at St Petersburg to the west, and also increased the range of the diurnal inequality of declination, the latter effect being the more conspicuous. Schuster,61 who has considered the evidence advanced by Leyst from the mathematical standpoint, considers it to be inconclusive.
§ 42. The best way of carrying out a magnetic survey depends on where it has to be made and on the object in view. The object that Magnetic probably still comes first in importance is a knowledge Surveys. of the declination, of sufficient accuracy for navigation
in. all navigable waters. One might thus infer that magnetic surveys consist mainly of observations at sea. This cannot however be said to be true of the past, whatever it may be of the future, and this for several reasons. Observations at sea entail the use of a ship, specially constructed so as to be free fromdisturbing influence, and so are inherently costly; they are also apt to be of inferior accuracy. It might be possible in quiet weather, in a large vessel free from vibration, to observe with instruments of the highest precision such as a unifilar magneto-meter, but in the ordinary surveying ship apparatus of less sensitiveness has to be employed. The declination is usually determined with some form of compass. The other elements most usually found directly at sea are the inclination and the total force, the instrument employed being a special form of inclinometer, such as the Fox circle, which was largely used by Ross in the Antarctic, or in recent years the Lloyd-Creak. This latter instrument differs from the ordinary dip-circle fitted for total force observations after H. Lloyd's method mainly in that the needles rest in pivots instead of on agate edges. To overcome friction a projecting pin on the framework is scratched with a roughened ivory plate.
The most notable recent example of observations at sea is afforded by the cruises of the surveying ships " Galilee " and " Carnegie " under the auspices of the Carnegie Institution of Washington, which includes in its magnetic programme a general survey. To see where the ordinary land survey assists navigation, let us take the case of a country with a long sea-board. If observations were taken every few miles along the coast results might be obtained adequate for the ordinary wants of coasting steamers, but it would be difficult to infer what the declination would be 50 or even 20 miles off shore at any particular place. If, however, the land area itself is carefully surveyed, one knows the trend of the lines of equal declination, and can usually extend them with considerable accuracy
many miles out to sea. One also can tell what
places if any on the coast suffer from local disturb-
ances, and thus decide on the necessity of special
observations. This is by no means the only immediately useful purpose which is or may be served by magnetic surveys on land. In Scandinavia use has been made of magnetic observations in prospecting for iron ore. There are also various geological and geodetic problems to whose solution magnetic surveys may afford valuable guidance. Among the most important recent surveys may be mentioned those of the British Isles by A. Rucker and T. E. Thorppe,6E of France and Algeria by Moureaux68 of Italy by Chistoni and Palazzo,64 of the Netherlands by Van Ryckevorsel,65 of South Sweden by Carlheim Gyllenskiold,66 of Austria-Hungary by Liznar,87 of Japan by Tanakadate,88 of the East Indies by Van Bemmelen, and South Africa by J. C. Beattie. A survey of the United States has been proceeding for a good many years, and many results have appeared in the publications of the U.S. Coast and Geodetic Survey, especially Bauer's Magnetic Tables and Magnetic Charts, 1908. Additions to our knowledge may also be expected from surveys of India, Egypt and New Zealand.
For the satisfactory execution of a land survey, the observers must have absolute instruments such as the unifilar magnetometer and dip circle, suitable for the accurate determination of the magnetic elements, and they must be able to fix the exact positions of the spots where observations are taken. If, as usual, the survey occupies several years, what is wanted is the value of the elements not at the actual time of observation, but at some fixed epoch, possibly some years earlier or later. At a magnetic observatory, with standardized records, the difference between the values of a magnetic element at any two specified instants can be derived from the magnetic curves. But at an ordinary survey station, at a distance from an observatory, the information is not immediately available. Ordinarily the reduction to a fixed epoch is done in at least two stages, a correction being applied for secular change, and a second for the departure from the mean value for the day due to the regular diurnal inequality and to disturbance.
The reduction to a fixed epoch is at once more easy and more accurate if the area surveyed contains, or has close to its borders, a well distributed series of magnetic observatories, whose records are corn, parable and trustworthy. Throughout an area of the size of France or Germany, the secular change between any two specified dates can ordinarily be expressed with sufficient accuracy by a formula of the type
S=do+a(l—lo)+b(X—Xo) . . (i),
where E denotes secular change, l latitude and a longitude, the letters with suffix o relating to some convenient central position. The constants So, a, b are to be determined from the observed secular changes at the fixed observatories whose geographical co-ordinates are accurately known. Unfortunately, as a rule, fixed observatories are few in number and not well distributed for survey purposes; thus the secular change over part at least of the area has usually to be found by repeating the observations after some years at several of the field stations. The success attending this depends on the
exactitude with which the sites can be recovered, on the accuracy of the observations, and on the success with which allowance is made for diurnal changes, regular and irregular. I t is thus desirable that the observations at repeat stations should be taken at hours when the regular diurnal changes are slow, and that they should not be accepted unless taken on days that prove to be magnetically quiet. Unless the secular change is exceptionally rapid, it will usually be most convenient in practice to calculate it from or to the middle of the month, and then to allow for the difference between the mean value for the month and the value at the actual hour of observation. There is here a difficulty, inasmuch as the latter part of the correction depends on the diurnal inequality, and so on the local tirne of the station. No altogether satisfactory method of surmounting this difficulty has yet been proposed. Rucker and Thorpe in their British survey assumed that the divergence from the mean value at any hour at any station might be regarded as made up of a regular diurnal inequality, identical with that at Kew when both were referred to local time, and of a disturbance element identical with that existing at the same absolute time at Kew. Suppose, for instance, that at hour h G.M.T. the departure at Kew from the mean value for the month is d, then the corresponding departure from the mean at a station X degrees west of Kew is d—e, where e is the in-crease in the element at Kew due to the regular diurnal inequality between hour h—a/15 and hour h. This procedure is simple, but is exposed to various criticisms. If we define a diurnal inequality as the result obtained by combining hourly readings from all the days of a month, we can assign a definite meaning to the diurnal inequality for a particular month of a particular year, and after the curves have been measured we can give exact numerical figures answering to this definition. But the diurnal inequality thus obtained differs, as has been pointed out, from that derived from a limited number of the quietest days of the month, not merely in amplitude but in phase, and the view that the diurnal changes on any individual day can be regarded as made up of a regular diurnal inequality of definite character and of a disturbance element is an hypothesis which is likely at times to be considerably wide of the mark. The extent of the error involved in assuming the regular diurnal inequality the same in the north of Scotland, or the west of Ireland, as in the south-east of England remains to be ascertained. As to the disturbance element, even if the disturbing force were of given magnitude and direction all over the British Isles—which we now know is often very far from the case—its effects would necessarily vary very sensibly owing to the considerable variation in the direction and intensity of the local undisturbed force. If observations were confined to hours at which the regular diurnal changes are slow, and only those taken on days of little or no disturbance were utilized, corrections combining the effects of regular and irregular diurnal changes could be derived from the records of fixed observations, supposed suitably situated, combined in formulae of the same type as (i).
§ 43. The field results having been reduced to a fixed epoch, it remains to combine them in ways likely to be useful. In most cases the results are embodied in charts, usually of at least two kinds, one set showing only general features, the other the chief local peculiarities. Charts of the first kind resemble the world charts (figs. i to 4) in being free from sharp twistings and convolutions. In these the declination for instance at a fixed geographical position on a particular isogonal is to be regarded as really a mean from a considerable surrounding area.
Various ways have been utilized for arriving at these terrestrial isomagnetics—as Rucker and Thorpe call them—of which an elaborate discussion has been made by E. Mathias.° From a theoretical standpoint the simplest method is perhaps that employed by Liznar for Austria-Hungary. Let 1 and a represent latitude and longitude relative to a certain central station in the area. Then assume that throughout the area the value E of any particular magnetic element is given by a formula
E = Eo+al+bX+cL +dX2+elX,
where Eo, a, br c, d, e are absolute constants to be determined from the observations. When determining the constants, we write for E in the equation the observed value of the element (corrected for secular change, &c.) at each station, and for l and X the latitude and longitude of the station relative to the central station. Thus each station contributes an equation to assist in determining the six constants. They can thus be found by least squares or some simpler method. In Liznar's case there were 195 stations, so that the labour of applying least squares would be considerable. This is one objection to the method. A second is that it may allow undesirably large weight to a few highly disturbed stations. In the case of the British Isles, Rucker and Thorpe employed a different method. The area was split up into districts. For each district a mean was formed of the observed values of each element, and the mean was assigned to an imaginary central station, whose geographical co-ordinates represented the mean of the geographical co-ordinates of the actual stations. Want of uniformity In the distribution of the stations may be allowed for by weighting the results. Supposing Eo the value of the element found for the central station of a district, it was assumed that the value E at any actual station whose latitude and longitude exceeded those of the central station by 1 and a was given by E = Eo+al+bX, with a and b constants throughout the
district. Having found Eo, a and b, Rucker and Thorpe calculated values of the element for points defined by whole degrees of longitude (from Greenwich) and half degrees of latitude. Near the common border of two districts there would be two calculated values, of which the arithmetic mean was accepted.
The next step was to determine by interpolation where isogonals —or other isomagnetic lines—cut successive lines of latitude. The curves formed by joining these successive points of intersection were called district lines or curves. Rucker and Thorpe's next step was to obtain formulae by trial, giving smooth curves of continuous curvature—terrestrial isomagnetics—approximating as closely as possible to the district lines. The curves thus obtained had somewhat complicated formulae. For instance, the isogonals south of 54°.5 latitude were given for the epoch Jan. 1, 1891 by
D=18° 37'-1-18'•5(1—49.5)—3'•5 cos 145°(1—49.5)}
+126'.3+1'•5(1—49'5)1(X—4)+0'•01(X—4)2(1—54'5)2,
where D denotes the westerly declination. Supposing, what is at least approximately true, that the secular change in Great Britain since 1891 has been uniform south of lat. 54°•5, corresponding formulae for the epochs Jan. 1, 1901, and Jan. 1, 1906, could be obtained by substituting for 18° 37' the values 17° 44' and 17° 24' respectively. In their very laborious and important memoir E. Mathias and B. Baillaud69 have applied to Rucker and Thorpe's. observations a method which is a combination of Rucker and Thorpe's and of Liznar's. Taking Rucker and Thorpe's nine districts, and the magnetic data found for the nine imaginary central stations, they employed these to determine the six constants of Liznar's formula. This is an immense simplification in arithmetic. The declination formula thus obtained for the epoch Jan. 1, :891, was
D =20° 45'•89+.53474a+•347161+.000021X2
+•0003431A— •00023912,
where 1+(53° 3o'•5) represents the latitude, and (X+5° 35''2) the west longitude of the station. From this and the corresponding formulae for the other elements, values were calculated for each of Rucker and Thorpe's 882 stations, and these were compared with the observed values. A complete record is given of the differences between the observed and calculated values, and of the corresponding differences obtained by Rucker and Thorpe from their own formulae. The mean numerical (calculated ..- observed) differences from the two different methods are almost exactly the same—being approximately to' for declination, 5'a for inclination, and 70y for horizontal force. The applications by Mathias° of his method to the survey data of France obtained by Moureaux, and those of the Netherlands obtained by van Rijckevorsel, appear equally successful. The method dispenses entirely with district curves, and the parabolic formulae are perfectly straightforward both to calculate and to apply; they thus appear to possess marked advantages. Whether the method could be applied equally satisfactorily to an area of the size of India or the United States actual trial alone would show.
§ 44. Rucker and Thorpe regarded their terrestrial isomagnetics and the corresponding formulae as representing the normal field that would exist in the absence of disturbances 4oca1 DIs-
peculiar to the neighbourhood. Subtracting the forces to .
calWs derived from the formulae from those observed, we
obtain forces which may be ascribed to regional disturbance.
When the vertical disturbing force is downwards, or the observed vertical component larger than the calculated, Rucker and Thorpe regard it as positive, and the loci where the largest positive values occur they termed ridge lines. The corresponding loci where the largest negative values occur were called valley lines. In the British Isles Rucker and Thorpe found that almost without exception, in the neighbourhood of a ridge line, the horizontal component of the disturbing force pointed towards it, throughout a considerable area on both sides. The phenomena are similar to what would occur if ridge lines indicated the position of the summits of under-ground masses of magnetic material, magnetized so as to attract the north-seeking pole of a magnet. Rucker and Thorpe were inclined to believe in the real existence of these subterranean magnetic mountains, and inferred that they must be of considerable extent, as theory and observation alike indicate that thin basaltic sheets or dykes, or limited masses of trap rock, produce no measurable magnetic effect except in their immediate vicinity. In support of their conclusions, Rucker and Thorpe dwell on the fact that in the United Kingdom large masses of basalt such as occur in Skye, Mull, Antrim, North Wales or the Scottish coalfield, are according to their survey invariably centres of attraction for the north-seeking pole of a magnet. Various cases of repulsion have, however, been described by other observers in the northern hemisphere.
§ 45. Rucker and Thorpe did not make a very minute examination of disturbed areas, so that purely local disturbances larger than any noticed by them may exist in the United Kingdom. But any that exist are unlikely to rival some that have been observed elsewhere, notably those in the province of Kursk in Russia described by Moureaux 7U and by E. Leyst.n In Kursk Leyst observed declinations varying from o° to 36o°, inclinations varying from 39°'1 to 90°; he obtained values of the horizontal force varying from o to 0.856 C.G.S., and values of the vertical force varying from 0.371 to 1.836. Another highly disturbed Russian district Krivoi Rog
(48 ° N. lat. 33° E. long.) was elaborately surveyed by Paul Passalsky.72 The extreme values observed by him differed, the declination by 282° 40', the inclination by 41° 53', horizontal force by 0.658, and vertical force by 1.358. At one spot a difference of 116°i was observed between the declinations at two positions only 42 metres apart. In cases such as the last mentioned, the source of disturbance comes presumably very near the surface. It is improbable that any such enormously rapid changes of declination can be experienced anywhere at the surface of a deep ocean. But in shallow water disturbances of a not very inferior order of magnitude have been met with. Possibly the most outstanding case known is that of an area, about 3 M. long by it m. at its widest, near Port Walcott, off the N.W. Australian coast. The results of a minute survey made here by H.M.S. " Penguin " have been discussed by Captain E. W. Creak." Within the narrow area specified, declination varied from 26° W. to 56° E., and inclination from 50° to nearly 80°, the observations being taken some 8o ft. above sea bottom. Another note-worthy case, though hardly comparable with the above, is that of East Loch Roag at Lewis in the Hebrides. A survey by H.M.S. " Research " in water about Ioo ft. deep—discussed by Admiral A. M. Field"--showed a range of 11° in declination. The largest observed disturbances in horizontal and vertical force were of the order 0.02 and o.05 C.G.S. respectively. An interesting feature in this case was that vertical force was reduced, there being a well-marked valley line.
In some instances regional magnetic disturbances have been found to be associated with geodetic anomalies. This is true of an elongated area including Moscow, where observations were taken by Fritsche." Again, Eschenhagen 76 detected magnetic anomalies in an area including the Harz Mountains in Germany, where deflections of the plumb line from the normal had been observed. He found a magnetic ridge line running approximately parallel to the line of no deflection of the plumb line.
§ 46. A question of interest, about which however not very much is known, is the effect of local disturbance on secular change and on the diurnal inequality. The determination of secular change in a highly disturbed locality is difficult, because an unintentional slight change in the spot where the observations are made may wholly falsify the conclusions drawn. When the disturbed area is very limited in extent, the magnetic field may reasonably be regarded as composed of the normal field that would have existed in the absence of local disturbance, plus a disturbance field arising from magnetic material which approaches nearly if not quite to the surface. Even if no sensible change takes place in the disturbance field, one would hardly expect the secular change to be wholly normal. The changes in the rectangular components of the force may possibly be the same as at a neighbouring undisturbed station, but this will not give the same change in declination and inclination. In the case of the diurnal in-equality, the presumption is that at least the declination and inclination changes will be influenced by local disturbance. If, for example, we suppose the diurnal inequality to be due to the direct influence of electric currents in the upper atmosphere, the declination change will represent the action of the component of a force of given magnitude which is perpendicular to the position of the compass needle. But when local disturbance exists, the direction of the needle and the intensity of the controlling field are both altered by the local disturbance, so it would appear natural for the declination changes to be influenced also. This conclusion seems borne out by observations made by Passalsky72 at Krivoi Rog, which showed diurnal inequalities differing notably from those experienced at the same time at Odessa, the nearest magnetic observatory. One station where the horizontal force was abnormally low gave a diurnal range of declination four times that at Odessa; on the other hand, the range of the horizontal force was apparently reduced. It would be unsafe to draw general conclusions from observations at two or three stations, and much completer information is wanted, but it is obviously desirable to avoid local disturbance when selecting a site for a magnetic observatory, assuming one's object is to obtain data reasonably applicable to a large area. In the case of the older observatories this consideration seems sometimes to have been lost sight of. At Mauritius, for instance, inside of a circle of only 56 ft. radius, having for centre the declination pillar of the absolute magnetic hut of the Royal Alfred Observatory, T. F. Claxton" found that the declination varied from 4° 56' to 13° 45' W., the inclination from 50° 21' to 58° 34' S., and the horizontal force from 0.197 to 0.244 C.G.S. At one spot he found an alteration of 1°3 in the declination when the magnet was lowered from 4 ft. above the ground to 2. Disturbances of this order could hardly escape even a rough investigation of the site.
§ 47. If we assume the magnetic force on the earth's surface derivable from a potential V, we can express V as the sum of two Gaussian series of solid spherical harmonics, one containing nega-Potentiat tive, the other positive integral powers of the radius and Con- vector r from the earth's centre. Let X denote east scants. longitude from Greenwich, and let µ=cos(47r—l), where 1 is latitude; and also let
H'" =(1 —µI) 1m µ" m—(n—m2()(211n—I)—112—1)µ"-m-2+ .
" ]'
where n and m denote any positive integers, m being not greater than n. Then denoting the earth's radius by R, we have V/R=(R/r)"+I[Hn(g"cosmT+hn sinmX)]
+2(r/R)"[H' (g_ n cos mX+h sin mX)],
where 2 denotes summation of m from o to n, followed by summation of n from o to co. In this equation gn, &c. are constants, those with positive suffixes being what are generally termed Gaussian constants. The series with negative powers of r answers to forces with a source internal to the earth, the series with positive powers to forces with an external source. Gauss found that forces of the latter class, if existent, were very small, and they are usually left out of account. There are three Gaussian constants of the first order, g1°, git, hit, five of the second order, seven of the third, and so on. The coefficient of a Gaussian constant of the nth order is a spherical harmonic of the nth degree. If R be taken as unit length, as is not infrequent, the first order terms are given by
V1=r-2[gi° sin l+(g11 cos a+h31 sin X) cos l].
The earth is in reality a spheroid, and in his elaborate work on the subject J. C. Adams 76 develops the treatment appropriate to this case. Here we shall as usual treat it as spherical. We then have for the components of the force at the surface
X = —R -1(1 —µ2)l (dV/dµ) towards the astronomical north, Y=—R-1(1—µ2) west, Z = —dV/dr vertically downwards.
Supposing the Gaussian constants known, the above formulae would give the force all over the earth's surface. To determine the Gaussian constants we proceed of course in the reverse direction, equating the observed values of the force components to the theoretical values involving g' , &c. If we knew the values of the component
forces at regularly distributed stations all over the earth's surface, we could determine each Gaussian constant independently of the others. Our knowledge however of large regions, especially in the Arctic and Antarctic, is very scanty, and in practice recourse is had to methods in which the constants are not determined independently. The consequence is unfortunately that the values found for some of the constants, even amongst the lower orders, depend very sensibly on how large a portion of the polar regions is omitted from the
gt° g11 hit
1842-1845 +•32173 +•02833 —'05820
1880 +•31611 +•02470 —•06071 Some of the higher constants were relatively much more affected. Thus, on the hypotheses of 48 and of 24 constants respectively, the values obtained for g2° in 1842-1845 were —.00127 and —•00057, and those obtained for hat in 188o were +•00748 and +•00573. It must also be remembered that these values assume that the series in positive powers of r, with coefficients having negative suffixes, is absolutely non-existent. If this be not assumed, then in any equation determing X or Y, g;; must be replaced by C. +8!„ and in any
equation determining Z by —In/ (n+ I) } gn ; similar remarks
apply to hn and . It is thus theoretically possible to check the truth of the assumption that the positive power series is non-existent by comparing the values obtained for gn and hn from the X and
Y or from the Z equations, when gm, and hn;,are assumed zero. If the values so found differ, values can be found for and h. which will harmonize the two sets of equations. Adams gives the values obtained from the X, Y and the Z equations separately for the
1829
Erman- 1830 1845 1880 1885 1885 1885
Petersen. Gauss. Adams. Adams. Neumayer. Schmidt. Fritsche.
gt° +32007 +•32348 +•32187 +•31684 -f •31572 +'31735 +•31635
gt1 + •02835 +.0311I +•02778 +•02427 +•02481 +•02356 +•02414
h3' —i —.06246 —•05783 —.06030 —•06026 —•05984 —.05914
•o6oi
calculations, and on the number of the constants of the higher orders which are retained.
Table XLIV. gives the values obtained for the Gaussian constants of the first order in some of the best-known computations, as collected by W. G. Adams.79
§ 48. Allowance must be made for the difference in the epochs, and for the fact that the number of constants assumed to be worth retaining was different in each case. Gauss, for instance, assumed 24 constants sufficient, whilst in obtaining the results given in the table J. C. Adams retained 48. Some idea of the uncertainty thus arising may be derived from the fact that when Adams assumed 24 constants sufficient, he got instead of the values in the table the following:
Gaussian constants. The following are examples of the values thence deducible for the coefficients of the positive power series:
g_10 g_i1 h-it g_4° g_5° g-8°
1842-1845 +'0018 -'0002 -'0014 +'0064 +'0072 +'0124 188o -•0002 -•0012 +•0015 -'0043 —•002I -'0013
Compared to g,°, gs° and g6° the values here found for g-4°, g-5° and g-e° are far from insignificant, and there would be no excuse for neglecting them if the observational data were sufficient and reliable. But two outstanding features claim attention, first the smallness of
g-i' and h-1', the coefficients least likely to be affected by observational deficiencies, and secondly the striking dissimilarity between the values obtained for the two epochs. The conclusion to which these and other facts point is that observational deficiencies, even up to the present date, are such that no certain conclusion can be drawn as to the existence or non-existence of the positive power series. It is also to be feared that considerable uncertainties enter into the values of most of the Gaussian constants, at least those of the higher orders. The introduction of the positive power series'necessarily improves the agreement between observed and calculated values of the force, but it is more likely than not to be disadvantageous physically, if the differences between observed values and those calculated from the negative power series alone arise in large measure from observational deficiencies.
Coefficients.
Epoch. Authority for North West M/R3 in
Constants. Latitude. Longitude. G.C.S. units.
° °
165o H. Fritsche . . 82 50 42 55 '3260
1836 78 27 63 35 •3262
1845 J. C. Adams . . 78 44 64 20 •3282
7 24 6 4 '3 34
1885 Neumayer-Petersen 67 3 •3224
and Bauer . 78 3
1885 Neumayer, Schmidt 78 34 68 31 '3230
§ 49. The first order Gaussian constants have a simple physical meaning. The terms containing them represent the potential arising from the uniform magnetization of a sphere parallel to a fixed axis; the moment M of the spherical magnet being given by
M = R3{(gi°)2 + (Or + (hl1)1l ,
where R is the earth's radius. The position of the north end of the axis of this uniform magnetization and the values of M/R3, derived from the more important determinations of the Gaussian constants, are given in Table XLV. The data for 165o are of some-what doubtful value. If they were as reliable as the others, one would feel greater confidence in the reality of the apparent movement of the north end of the axis from east to west. The table also suggests a slight diminution in M since 1845, but it is open to doubt whether the apparent change exceeds the probable error in the calculated values. It should be carefully noticed that the data in the table apply only to the first order Gaussian terms, and so only to a portion of the earth's magnetization, and that the Gaussian constants have been calculated on the assumption that the negative power series alone exists. The field answering to the first order terms—or what Bauer has called the normal field—constitutes much the most important part of the whole magnetization. Still what remains is very far from negligible, save for rough calculations. It is in fact one of the weak points in the Gaussian analysis that when one wishes to represent the observed facts with high accuracy one is obliged to retain so many terms that calculation becomes burden-some.
§ 50. The possible existence of a positive power series is not the only theoretical uncertainty in the Gaussian analysis. There is Earth-air the further possibility that part of the earth's magnetic Currents' field may not answer to a potential at all. Schmidt8'
in his calculation of Gaussian constants regarded this as a possible contingency, and the results he reached implied that as much as 2 or 3 of the entire field had no potential. If the magnetic force F on the earth's surface comes from a potential, then the line
integral f Fds taken round any closed circuit s should vanish. If the
integral does not vanish, it equals 4iI, where I is the total electric current traversing the area bounded by s. A-1- sign in the result of the integration means that the current is downwards (i.e. from air to earth) or upwards, according as the direction of integration round the circuit, as viewed by an observer above ground, has been clock-wise or anti-clockwise. In applications of the formula by W. von Bezold 81 and Bauer 82 the integral has been taken along parallels of latitude in the direction west to east. In this case a + sign indicates a resultant upward current over the area between the parallel of latitude traversed and the north geographical pole. The difference between the results of integration round two parallels of latitude gives the total vertical current over the zone between them. Schmidt's final estimate of the average intensity of the earth-air current, irrespective of sign, for the epoch 1885 was 0.17 ampere per
square kilometre. Bauer employing the same observational data as Schmidt, reached somewhat similar conclusions from the differences between integrals taken round parallels of latitude at 5° intervals from 60° N. to 60° S. H. Fritsche 83 treating the problem similarly, but for two epochs, 1842 and 1885, got conspicuously different results for the two epochs, Bauer 84 has more recently repeated his calculations, and for three epochs, 1842-1845 (Sabine's charts), 1880 (Creak's charts), and 1885 (Neumayer's charts), obtaining the mean value of the current per sq. km. for 5° zones. Table XLVI. is based on Bauer's figures, the unit being o'ooI ampere, and + denoting an upwardly directed current.
Latitude. Northern Hemisphere. Southern Hemisphere.
1842-5. 1880. 1885. 1842-5. 1880. 1885.
0° to 15° - I -32 -34 +66 + 30 + 36
I 5° , 0° - 70 -59 -68 + 2 - 62 - 63
3
30° „ 45° + 3 +14 -22 +26 — I I — 14
45° ,, 6o° -31 -21 +78 + 5 +276 +213
In considering the significance of the data in Table XLVI., it should be remembered that the currents must be regarded as mean values derived from all hours of the day, and all months of the year. Currents which were upwards during certain hours of the day, and downwards during others, would affect the diurnal inequality; while currents which were upwards during certain months, and down-wards during others, would cause an annual inequality in the absolute values. Thus, if the figures be accepted as real, we must suppose that between 15° N. and 30° N. there are preponderatingly down-ward currents, and between o° S. and 15° S. preponderatingly upward currents. Such currents might arise from meteorological conditions characteristic of particular latitudes, or be due to the relative distribution of land and sea; but, whatever their cause, any considerable real change in their values between 1842 and 1885 seems very improbable. The most natural cause to which to attribute the difference between the results for different epochs in Table XLVI. is unquestionably observational deficiencies. Bauer himself regards the results for latitudes higher than 45° as very uncertain, but he seems inclined to accept the reality of currents of the average intensity of 1/30 ampere per sq. km. between 45° N. and 45°S.
Currents of the size originally deduced by Schmidt, or even those of Bauer's latest calculations, seem difficult to reconcile with the results of atmospheric electricity (q.v.).
§ 51. There is no single parallel of latitude along the whole of which magnetic elements are known with high precision. Thus, results of greater certainty might be hoped for from the application of the line integral to well surveyed countries. Such applications have been made, e.g. to Great Britain by Riicker,86 and to Austria by Liznar,b8 but with negative results. The question has also been considered in detail by Tanakadate88 in discussing the magnetic survey of Japan. He makes the criticism that the taking of a line integral round the boundary of a surveyed area amounts to utilizing the values of the magnetic elements where least accurately known, and he thus considers it preferable to replace the line integral by the surface integral.
43rI= f f(dY/dx—dX/dy)dxdy.
He applied this formula not merely to his own data for Japan, but also to British and Austrian data of Rucker and Thorpe and of Liznar. The values he ascribes to X and Y are those given by the formulae calculated to fit the observations. The result reached was " a line of no current through the middle of the country; in Japan the current is upward on the Pacific side and downward on the Siberian side; in Austria it is upward in the north and downward in the south; in Great Britain upward in the east and downward in the west.” The results obtained for Great Britain differed considerably according as use was made of Rucker and Thorpe's own district equations or of a series of general equations of the type subsequently utilized by Mathias. Tanakadate points out that the fact that his investigations give in each case a line of no current passing through the middle of the surveyed area, is calculated to throw doubt on the reality of the supposed earth-air currents, and he recommends a suspension of judgment.
§ 52. A question of interest, and bearing a relationship to the Gaussian analysis, is the law of variation of the magnetic elements with height above sea-level. If F represent the value at sea-level, and F+SF that at height h, of any component of force answering to Gaussian constants of the nth order, then i +SF/F = (1 +h/R)-8-2, where R is the earth's radius. Thus at heights of only a few miles we have very approximately SF/F = — (n+2)h/R. As we have seen, the constants of the first order are much the most important, thus we should expect as a first approximation SX/X=SY/Y =SZ/Z=—3h/R. This equation gives the same rate of decrease in all three components, and so no change in declination or inclination. Liznar 88 (°) compared this equation with the observed results of his Austrian survey, subdividing his stations into three groups according
to altitude. He considered the agreement not satisfactory. It must be remembered that the Gaussian analysis, especially when only lower order terms are retained, applies only to the earth's field freed from local disturbances. Now observations at individual high level stations may be seriously influenced not merely by regional disturbances common to low level stations, but by magnetic material in the mountain itself. A method of arriving at the vertical change in the elements, which theoretically seems less open to criticism, has been employed by A. Tanakadate 68 If we assume that a potential exists, or if admitting the possibility of earth-air currents we assume their effort negligible, we have dX/dz=dZ/dx, dY/dz=dZ/dy. Thus from the observed rates of change of the vertical component of force along the parallels of latitude and longitude, we can deduce the rate of change in the vertical direction of the two rectangular components of horizontal force, and thence the rates of change of the horizontal force and the declination. Also we have dZ/dz=4,rp — (dX/dx +dY /dy), where p represents the density of free magnetism at the spot. The spot being above ground we may neglect p, and thus deduce the variation in the vertical direction of the vertical component from the observed variations of the two horizontal components in their own directions. Tanakadate makes a comparison of the vertical variations of the magnetic elements calculated in the two ways, not merely for Japan, but also for Austria-Hungary and Great Britain. In each country he took five representative points, those for Great Britain being the central stations of five of Rucker and Thorpe's districts. Table XLVII. gives the mean of the five values obtained. By method (i.) is meant the formula involving 3h/R, by method (ii.) Tanakadate's method as explained above. H, V, D, and I are used as defined in § 5. In the case of H and V unity represents 17.
Great Britain. Austria-Hungary. Japan.
Method. (i.) (ii.) (i.) (ii.) (i.) (ii.)
H — 8.1 — 6.7 — 10.1 — 8.7 — 13.9 — 14.0
V . -21.2 -19.4 -19.0 -18.1 -17.1 -17'4
D (west) .. — 0'•04 . . + 0'•10 .. — 0'•27
I I . .. — 0'•05 .. — 0'•06 0'•01
The — sign in Table XLVII. denotes a decrease in the numerical values of H, V and I, and a diminution in westerly declination. If we except the case of the westerly component of force—not shown in the table—the accordance between the results from the two .nethods in the case of japan is extraordinarily close, and there is no very marked tendency for the one method to give larger values than the other. In the case of Great Britain and Austria the differences between the two sets of calculated values though not large are systematic, the 3h/R formula invariably showing the larger reduction with altitude in both H and V. Tanakadate was so satisfied with the accordance of the two methods in Japan, that he employed his method to reduce all observed Japanese values to sea-level. At a few of the highest Japanese stations the correction thus introduced into the value of H was of some importance, but at the great majority of the stations the corrections were all insignificant.
§ 53. Schuster 87 has calculated a potential analogous to the Gaussian potential, from which the regular diurnal changes of the Sctruater's magnetic elements all over the earth may be derived.
&mist From the mean summer and winter diurnal variations
Di variation
urnal l of the northerly and easterly components of force during Potential 187o at St Petersburg, Greenwich, Lisbon and Bombay,
he found the values of 8 constants analogous to Gaussian constants; and from considerations as to the hours of occurrence of the maxima and minima of vertical force, he concluded that the potential, unlike the Gaussian, must proceed in positive powers of r, and so answer to forces external to the earth. Schuster found, however, that the calculated amplitudes of the diurnal vertical force inequality did not accord well with observation; and his conclusion was that while the original cause of the diurnal variation is external, and consists probably of electric :urrents in the atmosphere, there are induced currents inside the earth, which increase the horizontal components of the diurnal inequality while diminishing the vertical. The problem has also been dealt with by H. Fritsche,88 who concludes, in opposition to Schuster, that the forces are partly internal and partly external, the two sets being of fairly similar magnitude. Fritsche repeats the criticism (already made in the last edition of this encyclopaedia) that Schuster's four stations were too few, and contrasts their number with the 27 from which his own data were derived. On the other nand, Schuster's data referred to one and the same year, whereas Fritsche's are from epochs varying from 1841 to 1896, and represent in some cases a single year's observations, in other cases means from several years. It is clearly desirable that a fresh calculation should be made, using synchronous data from a considerable number of well distributed stations; and it should be done for at least two epochs, one representing large, the other small sun-spot frequency. The year 187o selected by Schuster had, as it happened, a sun-spotfrequency which has been exceeded only once since 1750; so that the magnetic data which he employed were far from representative of average conditions.
§ 54. It was discovered by Folgheraiter 89 that old vases from Etruscan and other sources are magnetic, and from combined observation and experiment he concluded that they acquired Magnet - their magnetization when cooling after being baked, and Man - retained it unaltered. From experiments, he derived Vases, &a formulae connecting the magnetization shown by new clay
vases with their orientation when cooling in a magnetic field, and applying these formulae to the phenomena observed in the old vases he calculated the magnetic dip at the time and place of manufacture. His observations led him to infer that in Central Italy inclination was actually southerly for some centuries prior to 600 B.C., when it changed sign. In 400 B.C. it was about 20° N. ; since loo B.C. the change has been relatively small. L. Mercanton 9° similarly investigated the magnetization of baked clay vases from the lake dwellings of Neuchatel, whose epoch is supposed to be from 600 to 800 B.C. The results he obtained were, however, closely similar to those observed in recent vases made where the inclination was about 63°N., and he concluded in direct opposition to Folgheraiter that inclination in southern Europe has not undergone any very large change during the last 2500 years. Folgheraiter's methods have been extended to natural rocks. Thus B. Brunhes 91 found several cases of day metamorphosed by adjacent lava flows and transformed into a species of natural brick. In these cases the clay has a determinate direction of magnetization agreeing with that of the volcanic rock, so it is natural to assume that this direction coincided with that of the dip when the lava flow occurred. In drawing inferences, allowance must of course be made for any tilting of the strata since the volcanic outburst. From one case in France in the district of St Flour, where the volcanic action is assigned to the Miocene Age, Brunhes inferred a southerly dip of some 75°. Until a variety of cases have been critically dealt with, a suspension of judgment is advisable, but if the method should establish its claims to reliability it obviously may prove of importance to geology as well as to terrestrial magnetism.
§ 55. Magnetic phenomena in the polar regions have received considerable attention of late years, and the observed results are of so exceptional a character as to merit separate consideration. One feature, the large amplitude of the regular diurnal polar ptreinequality, is already illustrated by the data for Jan aomena. Mayen and South Victoria Land in Tables VIII. to XI. In the case, however, of declination allowance must be made for the small size of H. If a force F perpendicular to the magnetic meridian causes a change AD in D then OD =F/H. Thus at the " Discovery's " winter quarters in South Victoria Land, where the value of H is only about 0.36 of that at Kew, a change of 45' in D would be produced by a force which at Kew would produce a change of only 16'. Another feature, which, however, may not be equally general, is illustrated by the data for Fort Rae and South Victoria Land in Table XVII. It will be noticed that it is the 24-hour term in the Fourier analysis of the regular diurnal inequality which is specially enhanced. The station in South Victoria Land—the winter quarters of the " Discovery " in 1902—1904—was at 77° 5i' S. lat.; thus the sun did not set from November to February (mid-summer), nor rise from May to July (midwinter). It might not thus have been surprising if there had been an outstandingly large seasonal variation in the type of the diurnal inequality. As a matter of fact, however, the type of the inequality showed exceptionally small variation with the season, and the amplitude remained large through-out the whole year. Thus, forming diurnal inequalities for the three midsummer months and for the three midwinter months, we obtain the following amplitudes for the range of the several elements92
D. H. V. I.
Midsummer 64'•I 577 58y 2'•87
Midwinter 26'•8 2$7 187 I' 23
The most outstanding phenomenon in high latitudes is the frequency and large size of the disturbances. At Kew, as we saw in § § 25, the absolute range in D exceeds 20' on only 12 % of the total number of days. But at the " Discovery's " winter quarters, about sun-spot minimum, the range exceeded I ° on 70%, 2 ° on 37%, and 3° on fully 15% of the total number of days. One day in 25 had a range exceeding 4°. During the three midsummer months, only one day out of 111 had a range under 1°, and even at midwinter only one day in eight had a range as small as 30'. The H range at the " Discovery's' station exceeded 1007 on 40% of the days, and the V range exceeded 1007 on 32 % of the days.
The special tendency to disturbance seen in equinoctial months in temperate latitudes did not appear in the " Discovery's " records in the Antarctic. D ranges exceeding 3° occurred on 11% of equinoctial days, but on 40 % of midsummer days. The preponderance of large movements at midsummer was equally apparent in the other elements. Thus the percentage of days having a V range over 2007 was 21 at midsummer, as against 3 in the four equinoctial months.
At the " Discovery's " station small oscillations of a few minutes' duration were hardly ever absent, but the character of the larger disturbances showed a marked variation throughout the 24 hours.
Those of a very rapid oscillatory character were especially numerous in the morning between 4 and 9 a.m. In the late afternoon and evening disturbances of a more regular type became prominent, especially in the winter months. In particular there were numerous occurrences of a remarkably regular type of disturbance, half the total number of cases taking place between 7 and 9 p.m. This " special type of disturbance " was divisible into two phases, each lasting on the average about 20 minutes. During the first phase all the elements diminished in value, during the second phase they increased. In the case of D and H the rise and fall were about equal, but the rise in V was about 32 times the preceding fall. The disturbing force—on the north pole—to which the first phase might be attributed was inclined on the average about 5 °Z below the horizon, the horizontal projection of its line of action being inclined about 41 °z to the north of east. The amplitude and duration of the disturbances of the " special type " varied a good deal ; in several cases the disturbing force considerably exceeded 200y. A somewhat similar type of disturbance was observed by Kr. Birkeland" at Arctic stations also in 1902-1903, and was called by him the " polar elementary " storm. Birkeland's record of disturbances extends only from October 1902 to March 1903, so it is uncertain whether " polar elementary " storms occur during the Arctic summer. Their usual time of occurrence seems to be the evening. During their occurrence Birkeland found that there was often a great difference in amplitude and character between the disturbances observed at places so comparatively near together as Iceland, Nova Zembla and Spitzbergen. This led him to assign the cause to electric currents in the Arctic, at heights not exceeding a few hundred kilometres, and he inferred from the way in which the phenomena developed that the seat of the disturbances often moved westward, as if related in some way to the sun's position. Contemporaneously with the " elementary polar " storms in the Arctic Birkeland found smaller but distinct movements at stations all over Europe; these could generally be traced as far as Bombay and Batavia, and sometimes as far as Christchurch, New Zealand. Chree,92 on the other hand, working up the 1902-1904 Antarctic records, discovered that.during the larger disturbances of the " special type " corresponding but much smaller movements were visible at Christchurch, Mauritius, Kolaba, and even at Kew. He also found that in the great majority of cases the Antarctic curves were specially disturbed during the times of Birkeland's " elementary polar " storms, the disturbances in the Arctic and Antarctic being of the same order of magnitude, though apparently of considerably different type.
Examining the more prominent of the sudden commencements of magnetic disturbances in 1902-1903 visible simultaneously in the curves from Kew, Kolaba, Mauritius and Christchurch, Chree found that these were all represented in the Antarctic curves by movements of a considerably larger size and of an oscillatory character. In a number of cases Birkeland observed small simultaneous movements in the curves of his co-operating stations, which appeared to he at least sometimes decidedly larger in the equatorial than the northern temperate stations. These he described as " equatorial " perturbations, ascribing them to electric currents in or near the plane of the earth's magnetic equator, at heights of the order of the earth's radius. It was found, however, by Chree that in many, if not all, of these cases there were synchronous movements in the Antarctic, similar in type to those which occurred simultaneously with the sudden commencements of magnetic storms, and that these Antarctic movements were considerably larger than those described by Birkeland at the equatorial stations. This result tends of course to suggest a somewhat different explanation from Birkeland's. But until our knowledge of facts has received considerable additions all explanations must be of a somewhat hypothetical character.
In 1831 Sir James Ross84 observed a dip of 89° 59' at 70° 5' N., 96° 46' W., and this has been accepted as practically the position of Magnetic the north magnetic pole at the time. The position of
Man the south magnetic pole in 184o as deduced from the
Poles. Antarctic observations made by the " Erebus " and " Terror " expedition is shown in Sabine's chart as about 73° 30' S., 147° 30' E. In the more recent chart in J. C. Adams's Collected Papers, vol. 2, the position is shown as about 73° 40' S., 147° 7' E. Of late years positions have been obtained for the south magnetic pole by the " Southern Cross " expedition of 1898-1900 (A), by the
Discovery " in 1902-1904 (B), and by Sir E. Shackleton's expedition 1908-1909 (C). These are as follow:
(A) 72° 40' S., 1520 30' E.
(B) 72° 51' S., 156° 25' E.
(C) 72° 25' S., 1550 16' E.
Unless the diurnal inequality vanishes in its neighbourhood, a some-what improbable contingency considering the large range at the " Discovery's " winter quarters, the position of the south magnetic pole has probably a diurnal oscillation, with an average amplitude of several miles, and there is not unlikely a larger annual oscillation. Thus even apart from secular change, no single spot of the earth's surface can probably claim to be a magnetic pole in the sense popularly ascribed to the term. It the diurnal motion were absolutely regular, and carried the point where the needle is vertical round a closed curve, the centroid of that curve—though a spot where the needle is never absolutely vertical—would seem to have the best
claim to the title. It should also be remembered that when the dip is nearly 90° there are special observational difficulties. There are thus various reasons for allowing a considerable uncertainty in positions assigned to the magnetic poles. Conclusions as to change of position of the south magnetic pole during the last ten years based on the more recent results(A), (B) and (C) would, for instance, possess a very doubtful value. The difference, however, between these re-cent positions and that deduced from the observations of 1840-1841 is more substantial, and there is at least a moderate probability that a considerable movement towards the north-east has taken place during the last seventy years.
See publications of individual magnetic observatories, • more especially the Russian (Annales de l'Observatoire Physique Central), the French (Annales du Bureau Central Meteorologique de France), and those of Kew, Greenwich, Falmouth, Stonyhurst, Potsdam, Wilhelmshaven, de Bilt, Uccle, O'Gyalla, Prague, Pola, Coimbra, San Fernando, Capo di Monte, Tiflis, Kolaba, Zi-ka-wei, Hong-Kong, Manila, Batavia, Mauritius, Agincourt (Toronto), the observatories of the U.S. Coast and Geodetic Survey, Rio de Janeiro, Melbourne.
In the references below the following abbreviations are used: B.A. = British Association Reports; Batavia =Observations made at the Royal . Observatory at Batavia; M.Z. = Meteorologische Zeitschrift, edited by J. Hann and G. Hellman; P.R S. =Proceedings of the Royal Society of London; P T. =Philosophical Transactions; R. = Repertorium fur Meteorologie, St Petersburg; T.M.=Terrestrial Magnetism, edited by L. A. Bauer; R.A.S. Notices=Monthly Notices of the Royal Astronomical Society. Treatises are referred to by the numbers attached to them; e.g. (I) p. loo means p. 1o0 of Walker's Terrestrial Magnetism.
1 E. Walker, Terrestrial and Cosmical Magnetism (Cambridge and London, 1866). 1'H. Lloyd, A Treatise on Magnetism General and Terrestrial (London, 1874). 2 E. Mascart, Traite de magnetisme terrestre (Paris, 1900). 3 L. A. Bauer, United Slates Magnetic Declination Tables and Isogonic Charts, and Principal Facts relating to the Earth's Magnetism (Washington, 1902). 4 Balfour Stewart, " Terrestrial Magnetism " (under " Meteorology "), Ency. brit. 9th ed. 6 C. Chree, " Magnetism, Terrestrial," Ency. brit. loth ed. M.Z. 1906, 23, p. 145. 7 (3) p. 62. 8K. Akad. van Wetenschappen (Amsterdam, 1895; Batavia, 1899, &e.). 9 Atlas des Erdmagnetismus (Riga, 1903). 1° (I) p. 16, &c. 11 Kolaba (Colaba) Magnetical and Meteorological Observations, 1896, Appendix Table II. 12 (I) p. 21. 13 Report for 1906, App. 4, see also (3) p. 102. 14 (I) p. 166. 16 Ergebnisse der mag. Beobachtungen in Potsdam, 1901, p. xxxvi. 18 U.S. Coast and Geodetic Survey Report for 1895, App. 1, &c. 17 T.M. 1, pp. 62, 89, and 2, p. 68. 13 (3) p. 45. 19 Die Elemente des Erdmagnetismus, pp. 704-108. 20 Zur taglichen Variation der mag. Deklination (aus Heft II. des Archivs des Erdmagnetismus) (Potsdam, 1906). 21 M.Z. 1888, 5, p. 225. 22 M.Z. 1904, 21, p. 129. 23 P.T. 202 A, p. 335. 23" Camb. Phil. Soc. Trans. 20, p. 165. 24 P.T. 208 A, p. 205. 26 P.T. 203 A, p. 151. 26 P.T. 171. p. 541; P.R.S. 63, p. 64. 27 R.A.S. Notices 6o, p. 142. 2s Rendiconti del R. 1st. Lomb. 1902, Series II. vol. 35. 29 R. 1889, vol. 12, no. 8. 3° B.A. Report, 1898, p. 80. 31 P.R.S. (A) 79, p 151. 32 P.T. 204 A, p. 373. 33 Ann. du Bureau Central Meteorologique, annee 1897, 1 Mem. p. B65. 34 P.T. 161, p. 307. 36 M.Z. 1895, 12, p. 321. 36' P.T. 1851, p. 123; and 1852, p. ro3, see also (4) § 38. 36 P.T. 159, p. 363. 37 (I) p. 92. 26 R.A.S. Notices 65, p. 666. 39 R.A.S. Notices, 65, pp. 2 and 538. 90 K. Akad. van Wetenschappen (Amsterdam, 1906) p. 266. 41 R.A.S. Notices 65, p. 520. 92 B.A. Reports, i88o, p. 201 and 1881, p. 463. 43 Anhang Ergebnisse der mag. Beob. in Potsdam, 1896. 44 M.Z. 1899, 16, p. 385. 46 P.T. 166, p. 387. 46 Trans. Can. Inst. 1898-1899, p. 345, and Proc. Roy. Ast. Soc. of Canada, 1902-1903, p. 74, 1904, p. xiv., &c. 47 R.A.S. Notices 65, p. 186. 4B T.M. 10, p. 1. 49 Expedition norvegienne de z899-Igoo (Christiania, 1901). b° Theses presentees a la Faculte des Sciences (Paris, 1903). 61 Nat. Tijdschrift voor Nederlandsch-Indie, 1902, p. 71. 62 Wied. Ann. 1882, ,p. 336.
63 Sitz. der k. preuss. Akad. der Wiss., 24th June 1897, e.
64 T.M. 12, p. 1. 66 P.T. 143, p. 549; St Helena Observations, vol. ii., p. cxlvi., &c., (1) § 62. 66 Trans. R.S.E. 24, p. 669. b7 P.T. 178 A, p. 1. S8 Batavia, vol. 16, &c. 69 Batavia, Appendix to vol. 26. 66 R. vol. 17, no. I. 61 T.M. 3, p. 13, &c. 82 P.T. 181 A, p. 53 and 188 A. 63 Ann. du Bureau Central Met. vol. i. for years 1884 and 1887 to 1895. 64 Ann. dell' Uff. Centrale Met. e Geod. vol. 14, pt. i. p. 57. 66 A Magnetic Survey of the Netherlands for the Epoch 1st Jan. 141 (Rotterdam, 1895). 66 Kg. Svenska Vet. Akad. Handlingar, 1895, vol. 27, no. 7. 67 Denkschriften der math. naturwiss. Classe der k. Akad. des Wiss. (Wien), vols. 62 and 67. 88 Journal of the College of Science, Tokyo, 1904, vol. 14. 89 Ann. de l'observatoire
de Toulouse, 1907, vol. 7. 7° Ann. du Bureau Central Met. 1897, I. p. B36. 71 T.M. 7, p. 74. 72 Bull. Imp. Univ. Odessa 85, p. 1, and T.M. 7, p. 67. 73 P.T. 187 A, p. 345. 74 P.R.S. 76 A, p. 181. 76 Bull. Soc. Imp. des Naturalistes de Moskau, 1893, no. 4, p. 381, and T.M. 1, p. 50. 76 Forsch. zur dent. Landes- u. Volkskunde, 1898, Bd. xi, 1, and T.M. 3, p. 77. 77 P.R.S. 76 A, p. 507. 76 Adams, Scientific Papers, II. p. 446. 79 B.A. Report for 1898, p. 1 $0 Abhand. der bayer. Akad. der Wiss., 1895, vol. 19. 81 Sitz. k. Akad. der Wiss. (Berlin), 1897, no. xviii., also T.M. 3, p. 191. 62 T.M. 2, p. I I. 83 Die Elemente des Erdmagnetismus (St Petersburg,
1899), p. 103. 84 T.M. 9, p. 113. 88 T.M. 1, p. 77, and Nature, 57, pp. 16o and 180. 88 M.Z. 15, p. 175. 8" Sitz. der k. k. Akad. der Wass. Wien, math. nat. Classe, 1898, Bd. cvii., Abth. P.T. (A) 18o, p. 467. 88 Die Tagliche Periode der erdmagnetischen Elemente (St Petersburg, 1902). 89 R. Accad. Lincei Atli, viii. 1899, pp. 69, 121, 176, 269 and previous volumes, see also Seances de la Soc. Franc. de Physique, 1899, p. 118. 90 Bull. Soc. Vaud., Sc. Nat. 1906, 42, p. 225. 9' Comptes rendus, 1905, 141, p. 567. " National Antarctic Expedition 1901-1904, " Magnetic Observations." 93 The Norwegian Aurora Polaris Expedition 1902-1903, vol, i. 94 (I)
p. 163. (C. CII.)